Solve for $x$ and $y$ using elimination. ${-6x-y = -60}$ ${5x+y = 51}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. $-x = -9$ $\dfrac{-x}{{-1}} = \dfrac{-9}{{-1}}$ ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {-6x-y = -60}\thinspace$ to find $y$ ${-6}{(9)}{ - y = -60}$ $-54-y = -60$ $-54{+54} - y = -60{+54}$ $-y = -6$ $\dfrac{-y}{{-1}} = \dfrac{-6}{{-1}}$ ${y = 6}$ You can also plug ${x = 9}$ into $\thinspace {5x+y = 51}\thinspace$ and get the same answer for $y$ : ${5}{(9)}{ + y = 51}$ ${y = 6}$